Crystal-field excitations in uranium dioxide

The energy levels of the configuration f² in an eight-fold cubic crystal field (CF) have been calculated, and the results are used to explain the experimental spectrum of UO₂. The fourth-order CF potential turns out to be much smaller than usually assumed for this compound. This has an effect of reducing the J-mixing in the wavefunctions, particularly in the case of the ground state wavefunction. In spite of the strength of the CF, the ground state ³H₄T₂ is found to be modified only slightly be the J-mixing effect; it consists of 89.4% ³He₄, and the remaining eleven components make up the rest. Very good correlation is obtained between the experimental and simulated energy-level schemes. The predominance of ³H₄ in the ground state consequently increases the value of the calculated effective magnetic moment. The results are compared with our previous predictions about the system, and relevant conclusions drawn in the light of experimental data now available.     

Irradiation-induced heterogeneous nucleation in uranium dioxide

Using classical molecular dynamics simulations, we have studied the first stages of defect cluster formation resulting from 10 keV displacement cascades in uranium dioxide. Nanometre size cavities and dislocation loops are shown to appear as a result of the irradiation process. A specifically designed TEM experiment involving He implanted thin foils have also been carried out to support this modelling work. These results, in conjunction with several other observations taken from the literature of ion implanted or neutron irradiated uranium dioxide, suggest a radiation damage controlled heterogeneous mechanism for insoluble fission product segregation in UO₂.     

Electrochemical effects of isolated voids in uranium dioxide

We present a model to study the electrochemical effects of voids in oxide materials under equilibrium conditions and apply this model to uranium dioxide. Based on thermodynamic arguments, we claim that voids in uranium dioxide must contain oxygen gas at a pressure that we determine via a Kelvin equation in terms of temperature, void radius and the oxygen pressure of the outside gas reservoir in equilibrium with the oxide. The oxygen gas within a void gives rise to ionosorption and the formation of a layer of surface-charge on the void surface, which, in turn, induces an influence zone of space charge into the matrix surrounding the void. Since the space charge is carried in part by atomic defects, it is concluded that, as a part of the thermodynamic equilibrium of oxides containing voids, the off-stoichiometry around the void is different from its remote bulk value. As such, in a uranium dioxide solid with a void ensemble, the average off-stoichiometry level in the material differs from that of the void-free counterpart. The model is applied to isolated voids in off-stoichiometric uranium dioxide for a wide range of temperature and disorder state of the oxide.     

Elementary excitations in uranium dioxide: Unravelling the tangle

In solids with d- and f-electrons, under certain conditions the orbitals align to form an ordered structure. Collective excitations breaking this arrangement can take the form of oscillations of electric quadrupoles, the so-called quadrupolar waves. These represent a propagating pattern of charge densities implying a modulation of quadrupolar moments. Quadrupolar waves constitute a major component of the dynamics of uranium dioxide in its magneto-quadrupolar ordered phase. Together with spin-waves and phonons, these produce a very complex spectrum of elementary excitations having hybrid character over most of the Brillouin zone. Although neutron scattering spectra only reveal the tip of the iceberg of this spectrum, its complete and detailed modelling is needed to understand such experiments. Distinct roles of Jahn–Teller and superexchange mechanisms as sources of quadrupolar interactions can be clearly identified by such modelling.     

Quadrupolar interactions in TmCu

A thorough study of the cubic rare-earth intermetallic compound TmCu has been performed in the paramagnetic phase in order to obtain reliable quadrupolar parameters. The two (tetragonal and trigonal) symmetry-lowering modes have been systematically investigated by means of all the available experiments: parastriction, elastic constants, third-order magnetic susceptability and magnetization curves. Complete consistency is found between the various determinations of the magnetoelastic and quadrupolar exchange parameters. As in other isomorphous compounds, these quadrupolar interactions appear to be strong enough to compete with the bilinear interactions.     

Quadrupolar transfer pathways

A set of graphical conventions called quadrupolar transfer pathways is proposed to describe a wide range of experiments designed for the study of quadrupolar nuclei with spin quantum numbers I=1, 3/2, 2, 5/2, etc. These pathways, which inter alea allow one to appreciate the distinction between quadrupolar and Zeeman echoes, represent a generalization of the well-known coherence transfer pathways. Quadrupolar transfer pathways not merely distinguish coherences with different orders -2I < or = p< or = +2I, but allow one to follow the fate of coherences associated with single transitions that have the same coherence order p=m(I)(r)-m(I)(s) but can be distinguished by a satellite order q=(m(I)(r))(2)-(m(I)(s))(2).     

Phase transitions in uranium dioxide at high pressures and temperatures

The melting curve is plotted for uranium dioxide with fluorite structure in a pressure range from ?2.5 to +100 GPa. This curve has a peak at the point 3348 K, 6 GPa, and has a negative derivative at high pressures. The pressure corresponding to a polymorphic transition of uranium dioxide (37 GPa) at a temperature of 1015 K is determined. The slope of the equilibrium curve of the polymorphic transition in UO₂ in the temperature range 300–1000 K is ? 56 K/GPa.     

High-temperature transition of uranium dioxide to the super-ion state

A microscopic model of the high-temperature (T≈2670 K) phase transition of uranium dioxide to the super-ion state is developed. It is shown that accounting for the interaction of the point defect subsystem with the electron subsystem in the mean-field approximation (where this interaction leads to significant additional screening of the charge of some of the defects) and then calculating the configurational entropy of the point defects with allowance for the actual symmetry of the UO₂ crystalline lattice affords satisfactory agreement with the available experimental data on the degree of disorder of the anion sublattice and the behavior of the specific heat of uranium dioxide in the given temperature range. Zh. éksp. Teor. Fiz. 111, 585–599 (February 1997)     

Molecular dynamics studies of displacement cascades in the uranium dioxide matrix

In the context of studies on long-time storage of irradiated spent fuel, molecular dynamics simulations have been carried out in order to understand the physical phenomena, on the atomic scale, linked to modifications and damage that the uranium dioxide structure undergoes during α-decay irradiation in repository conditions. Simulations of atomic displacement cascades over an energy range from 1 to 20?keV for the initial primary knock-on atom (PKA) do not show any amorphization of the structure in agreement with what has been found experimentally, and there is very little correlation between the initial orientation of the PKA and the cascade morphology. The number of Frenkel pairs, as a function of the initial energy of the PKA, exhibits a power-law behaviour with an exponent of 0.9 which is contrary to the theoretical linear Norgett–Robinson–Torrens law. Finally, for both species the vacancies have a tendency to aggregate and cluster near the core of the cascade while interstitial atoms are preferentially located at the periphery of the branches corresponding to subcascades.     

Oxygen diffusion in uranium dioxide in the temperature range of phase transitions

The structure of and oxygen diffusion in UO₂ are studied by the molecular dynamics method in the range of transition to the superionic state (melting of the oxygen sublattice) and near the melting point of UO₂. The temperature dependence of the diffusion coefficient of a doubly charged oxygen ion in UO₂ is constructed. In the crystalline state at temperatures between 1800 and 2600 K, this dependence is described by an exponential dependence with a diffusion activation energy of 2.6±0.2 eV. In the superionic state (2600–3100 K), the activation energy of diffusion of an oxygen anion decreases to 1.88±0.13 eV. In melt (3100–3600 K), the exponential dependence of the diffusion coefficient of O^2- persists but the activation energy of diffusion decreases still further, to 0.8±0.2 eV. Our experimental results agree (within the limits of experimental error) with data on oxygen diffusion in the crystalline phase obtained by other researchers.     

Quadrupolar interaction around Ga in aluminium

N.M.R. C.W. measurements at 1.4 K performed on dilute alloys of Al-Ga are presented. An interpretation of available N.M.R. results obtained in this alloy is given, which shows a minimum of the electric field gradient at the second and third nearest neighbour sites.     

Formation energies and swelling of uranium dioxide by point defects

Hybrid density functional theory is used to study the stability and behavior of rare gases in uranium dioxide. Three insertion sites are considered: the octahedral interstitial position and the oxygen and uranium substitution sites. The optimized lattice constant, the volume variation induced by gaseous atom incorporation, and the defect formation energy are studied for each rare gas. Both lattice constants and formation energies increase with increase in radii of the rare gases. The octahedral interstitial position is the most favorable occupation site. The formation energy is found to be negative only for He at an interstitial site.     

On the cohesive energy and charge density of uranium dioxide

Self-consistent band structure calculations have been used to calculate the cohesive energy of UO₂. The computed cohesive energy was 1.641 Ry/formula unit compared with an experimental value of 1.614 Ry/formula unit. The self consistent charge density has been compared with free atom charge densities to illustrate the formation of bonding charge between the atoms.     

GGA+U study of the incorporation of iodine in uranium dioxide

Ab initio calculations based on the Density Functional Theory are carried out in order to investigate the incorporation of iodine in uranium dioxide. The GGA+U approximation is used to describe the strong correlations of uranium 5f electrons. We studied several defects that are likely to accommodate the incorporation of iodine in the material, such as uranium and oxygen vacancies, divacancy and Schottky defects. We find the iodine atoms to be stable in a neutral Schottky defects, with an incorporation energy of -1.3 eV. This result may account for the solubility of iodine in uranium dioxide observed experimentally. We also notice that the incorporation of iodine involves steric and electronic contributions. The larger the defect iodine is incorporated in, the lower is its incorporation energy. Besides, we find iodine to be charged -1, thus getting the stable electronic configuration of rare gases. We also highlight the fact that the use of GGA+U increases the number of metastable states (non global energy minima), compared to the LDA/GGA approximations. Consequently, special care has to be taken on the 5f electronic occupancies in order to ensure that the absolute energy minimum has been reached.     

INEPT Experiments Involving Quadrupolar Nuclei in Solids

Coherence transfer from quadrupolar²⁷Al (I= ) nuclei to³¹P (I= ) via INEPT experiments is investigated.²⁷Al →³¹P INEPT experiments on a (CH₃)₃P–AlCl₃complex in zeolite NaX are performed, and the results demonstrate that the³¹P INEPT signals strongly depend on whether or not the²⁷Al pulses are applied synchronously with the rotor period, and on the length of the²⁷Al pulses. A density-matrix calculation involving the use of the spin operators for spin and nuclei has been performed to help understand the evolution behavior of the density matrix under the influence of the quadrupolar interaction, the dipolar andJ-couplings, and the pulse lengths applied to the quadrupolar nuclei. The theoretical predictions obtained from these calculations are consistent with the INEPT experimental observations.     

Peculiarities of Quadrupolar Relaxation in Electrolyte Solutions

Peculiarities of quadrupolar relaxation in electrolyte solutions were established via comparison of the data obtained from proton and deuteron resonances. It has been shown that quadrupole coupling constants (QCC) of deuterons depend not only on internal electron structure of molecule or ion, but on solution structure as well. To interpret the experimental results quantum-chemical calculations of QCC of deuterons in different molecular complexes simulating different solution substructures were carried out. Density functional theory (DFT) method with hybrid B3LYP functional was used for all calculations.     

Quadrupolar matter-wave soliton in two-dimensional free space

We study two-dimensional (2D) matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupole–quadrupole interaction (QQI) in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross–Pitaevskii Equation (GPE). We find that the QQI solitons have a higher mass (smaller size and higher intensity) and stronger anisotropy than the dipole–dipole interaction (DDI) solitons under the same environmental parameters. Anisotropic soliton–soliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity.